Preface

Appendix 2

Dimensions of the Velocity of light

The following statement by Dr. W. D. Parkinson is repeated from the 1981 Sydney Symposium on the Expanding Earth.

"One of the reasons for introducing S.I. units was the incompatibility of e.m.u. and e.s.u. Electromagnetic units are based on the magnetic pole (m) such that the force of interaction is:

There is another way out of this impasse. If length and time are assigned the same dimensions, say L, then the discrepancy disappears. All physical quantities can then be expressed by the two dimensions M and L only. We must then redefine the unit of time. If this is taken as the "light-meter", i.e. the time taken for light to travel one meter in vaccuo, then velocity is non-dimensional, being a fraction of c (the quantity usually expressed by b in relativity theory)."

The dimensional equivalence of distance and time is implied by the null Universe, because every increment of mass implies an equal increment of energy, that is, mass M equals energy ML²T^-2. Cancelling M leaves L²=T².

An important consequence of Parkinson's simplification also is that mass, momentum, and potential energy have the same dimensions. The significance of this revision goes far beyond the elegant removal of the incompatibility of the electromagnetic and electrostatic units, which hitherto had been adjusted by an arbitrary improbable fiddle. Indeed, the dimensional equivalence of length and time is implied by the four-dimensional space-time of relativity, where time and distance are interchangeable; whereas the co-ordinates were written in the form, x, y, z, and i ct (i is the imaginary square root of minus one which appears in the four-dimensional equations); t now has the same dimensions as the other three, c is a pure number, and i is attachable equally to any one of the four.

The reduction of fundamental dimensions from four to two is a step towards Eddington's philosophical hope of linking universal constants to reduce their number, hopefully to a mutually cancelling pair, and towards Milne's ideal cosmology which has no constants with dimensions, and also towards Einstein's faith that all universal constants should have logical inevitability, and that no dimensionless constants should be arbitrary.

By Parkinson's simplification, the velocity of light c becomes a pure number like p and e, whose values are absolutely determined, p geometrically, and e arithmetically. Two pure numbers, the velocity of light and absolute zero, are the physical limits of existence, because mass, energy, temperature, resistivity, viscosity, and entropy tend toward infinity as velocity tends toward c, and at absolute zero all except mass-energy become zero, and it is not clear what happens to mass-energy at this singularity. Perhaps they mutually cancel to zero, making "absolute zero" truly absolute.

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